scholarly journals Intuitionistic fuzzy stability of Jensen-type quadratic functional equations

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 663-676 ◽  
Author(s):  
Zhihua Wang ◽  
Themistocles Rassias ◽  
Reza Saadati
Keyword(s):  
Real Number ◽  
Functional Equations ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Intuitionistic Fuzzy ◽  
Nonzero Real Number ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Stability Results

In this paper, we prove some stability results for Jensen-type quadratic functional equations 2f (x+y/2)+ 2f (x-y/2) = f (x) + f (y), f (ax+ay) + f (ax-ay) = 2a2f(x) + 2a2 f(y) in intuitionistic fuzzy normed spaces for a nonzero real number a with a ? ?1/2

scholarly journals Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN spaces

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3063
Author(s):  
Kandhasamy Tamilvanan ◽  
Abdulaziz Mohammed Alanazi ◽  
John Michael Rassias ◽  
Ali H. Alkhaldi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Quadratic Mapping ◽  
Normed Spaces ◽  
Intuitionistic Fuzzy ◽  
Fixed Point Techniques ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Stability Results

In this paper, we use direct and fixed-point techniques to examine the generalised Ulam–Hyers stability results of the general Euler–Lagrange quadratic mapping in non-Archimedean IFN spaces (briefly, non-Archimedean Intuitionistic Fuzzy Normed spaces) over a field.

scholarly journals Stability of Various Functional Equations in Non-Archimedean Intuitionistic Fuzzy Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Syed Abdul Mohiuddine ◽  
Abdullah Alotaibi ◽  
Mustafa Obaid
Keyword(s):  
Normed Space ◽  
Functional Equations ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
The Stability ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Stability Results

We define and study the concept of non-Archimedean intuitionistic fuzzy normed space by using the idea oft-norm andt-conorm. Furthermore, by using the non-Archimedean intuitionistic fuzzy normed space, we investigate the stability of various functional equations. That is, we determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framework of non-Archimedean IFN spaces.

scholarly journals Intuitionistic Fuzzy Stability of Functional Equations Associated with Inner Product Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Zhihua Wang ◽  
Themistocles M. Rassias
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Inner Product ◽  
Product Spaces ◽  
Normed Spaces ◽  
Inner Product Spaces ◽  
Intuitionistic Fuzzy ◽  
Stability Of Functional Equations ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Stability Results

In intuitionistic fuzzy normed spaces, we investigate some stability results for the functional equation which is said to be a functional equation associated with inner products space.

scholarly journals On the probabilistic stability of some functional equations

2013 ◽  
Vol 29 (1) ◽  
pp. 125-132
Author(s):  
CLAUDIA ZAHARIA ◽  
◽  
DOREL MIHET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Of Functional Equations ◽  
The Stability ◽  
Stability Results

We establish stability results concerning the additive and quadratic functional equations in complete Menger ϕ-normed spaces by using fixed point theory. As particular cases, some theorems regarding the stability of functional equations in β - normed and quasi-normed spaces are obtained.

scholarly journals An additive-quadratic functional equation in intuitionistic fuzzy normed spaces

10.26524/cm83 ◽  
2020 ◽  
Vol 4 (2) ◽  
Author(s):  
Soundararajan S ◽  
Suresh Kumar M ◽  
Sudhakar R
Keyword(s):  
Functional Equation ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Intuitionistic Fuzzy ◽  
The Stability ◽  
Intuitionistic Fuzzy Normed Spaces

In this work, we investigate the stability of additive-quadratic (AQ) functional equation in intuitionistic fuzzy normed spaces

scholarly journals On the stability problem of quadratic functional equations in 2-Banach spaces

2017 ◽  
pp. 5054-5061
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Stability Problem ◽  
Functional Equations ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability ◽  
Stability Results

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and G·avruta for the quadratic functional equation:f(2x + y) + f(2x ¡ y) = 2f(x + y) + 2f(x ¡ y) + 4f(x) ¡ 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by thequadratic functional equation in normed spaces to 2-Banach spaces.

A FIXED POINT APPROACH TO THE STABILITY OF GENERAL QUADRATIC EULER-LAGRANGE FUNCTIONAL EQUATIONS IN INTUITIONISTIC FUZZY SPACES

2016 ◽  
pp. 4430-4436
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Fixed Point Approach ◽  
Intuitionistic Fuzzy ◽  
The Stability ◽  
Lagrange Functional ◽  
Intuitionistic Fuzzy Normed Spaces

In this paper, we prove the generalized Hyers-Ulam stability of a general k-quadratic Euler-Lagrange functional equation:for any fixed positive integer in intuitionistic fuzzy normed spaces using a fixed point method.

scholarly journals Generalized ideal convergence in intuitionistic fuzzy normed linear spaces

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 811-820 ◽  
Author(s):  
Bipan Hazarika ◽  
Vijay Kumar ◽  
Bernardo Lafuerza-Guilién
Keyword(s):  
Real Number ◽  
Normed Spaces ◽  
Real Numbers ◽  
Ideal Convergence ◽  
Linear Spaces ◽  
Intuitionistic Fuzzy ◽  
Cauchy Sequences ◽  
Positive Integers ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Cluster Points

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In [19], Kostyrko et al. introduced the concept of ideal convergence as a sequence (xk) of real numbers is said to be I-convergent to a real number e, if for each ? > 0 the set {k ? N : |xk - e| ? ?} belongs to I. The aim of this paper is to introduce and study the notion of ?-ideal convergence in intuitionistic fuzzy normed spaces as a variant of the notion of ideal convergence. Also I? -limit points and I?-cluster points have been defined and the relation between them has been established. Furthermore, Cauchy and I?-Cauchy sequences are introduced and studied. .

Sign in / Sign up

Export Citation Format

Share Document